Roberto Firmino and Mohamed Salah scored the goals for the home side after Wissam Ben Yedder had given the visitors a surprise early lead, but Joaquin Correa ensured the LaLiga side left with a point.
Philippe Coutinho, heavily linked with a move to Barcelona during the transfer window, made his first appearance of the season at club level as a late substitute but it was not enough to inspire one last turnaround as Joe Gomez was shown a second yellow card for a foul on Correa in second-half stoppage time.
The match was a repeat of the Europa League final of 2016, in which Sevilla came from a goal down to win 3-1, but manager Jurgen Klopp insisted this week Liverpool had grown since that defeat in Basle.
The Reds were certainly the stronger of the teams for the majority and were deservedly heading for three points after Firmino and a fortuitous Salah strike had overturned Ben Yedder's fifth-minute opener.
Firmino missed a penalty at the end of the first half but Liverpool continued to look the better of the sides, producing a vastly improved performance from the 5-0 Premier League hammering by Manchester City last Saturday.
However, Correa made the most of some slack defending to rescue a share of the spoils for Eduardo Berizzo's side, who remain unbeaten in 2017-18.
Liverpool fans would have anticipated a typically fast start but it was Sevilla who opened the scoring with only five minutes played.
Some neat interplay between Correa and Sergio Escudero allowed the full-back to find space to the left of the area, and when Dejan Lovren completely missed his attempted clearance, Ben Yedder had a tap-in from less than six yards out.
The Reds came close to a prompt equaliser through Sadio Mane, whose low strike from the edge of the area was well saved by Sergio Rico, before Firmino headed Jordan Henderson's cross narrowly over.
But Firmino made no mistake in the 21st minute, the Brazilian converting from six yards after former Sevilla man Alberto Moreno's low cross eluded the defence and Rico at the near post.
The frantic early pace began to drop as each side looked to gain a greater control in possession but, eight minutes before half-time, Liverpool struck again.
Salah, having been fortunate to escape conceding a free-kick for tripping Steven N'Zonzi outside the Sevilla box, saw his low strike take a huge deflection off Simon Kjaer and nestle into the net beyond the helpless Rico.
Firmino had a golden chance to make it 3-1 before the break after Nico Pareja wrestled Mane to ground in the area, but his nonchalant penalty struck the outside of the right-hand post.
Liverpool continued to look the more likely to find the fourth and Sevilla's task became more difficult when Berizzo was sent to the stands for preventing Gomez from taking a quick throw-in.
However, with 18 minutes to play, Sevilla snatched an equaliser with their first shot of the second half. Substitute Luis Muriel fed Correa, who was granted a free path through the Liverpool defence to curl a good finish past Loris Karius from just inside the area.
Klopp immediately introduced Coutinho from the bench to a largely warm reception from the home fans, but the Brazilian could not conjure any late magic to give Liverpool a win.
Indeed, the match finished in tough circumstances for the hosts, who had Gomez sent off for a second yellow card just moments after Muriel missed a great chance to steal all three points.